RetroGaming

After watching some of a playthrough on YouTube, the PC Engine version looks fairly close to the original arcade game (also called Valkyrie no Densetsu/Legend of the Valkyrie). The Famicom game (called Valkyrie no Boken: Toki no Kagi no Densetsu/Valkyrie's Adventure: Legend of the Key of Time) is very different. The two games really only share the title (sort of) and a little backstory.

Legend of the Valkyrie is an on-rails multi-direction shooting game with light RPG elements. The most similar games I can think of are the D&D beat-em-up games Tower of Doom and Shadow Over Mystara, which were also originally arcade games.

But the Famicom's Valkyrie's Adventure is a ridiculously open world action RPG. The player is dropped in the middle of the wilderness with a sword and no idea of what to do first. You're free to walk in any direction, like most home 2D action RPGs. There's virtually no text, and many "puzzles" which involve using particular items in particular one-tile spaces (without any clues or hints). There's a guide in the original Famicom manual that will get you part-way through the game, but from there you're on your own.